In 1973, Black and Scholes derived the analytical expression for fixed-volatility option price by solving stochastic differential equations  [1]}. Financial mathematics applicated in derivative pricing has made great progress from then on  [2]}, [3]}. Recently, more complex options have emerged in financial engineering, which collectively called exotic options. An exotic option is the one attached some conditions to an ordinary option, set some barrier for example: when the underlying price reaches this barrier, the option contract will be activated, which is called knock-in option; when the underlying price reaches this barrier, the option contract is invalid, which is call konck-out option. Snyder had discussed down-and-out option in 1969  [4]}. Baaquie et al discussed this kind of option by path integral method, and derived the corresponding analytical expression  [5]}. Similar to one-dimensional infinite square potential well in quantum mechanics, they derived the analytical expression for double-knock-out option price  [6]}, which is in accordance with the result derived by mathematical method  [7]}. In addition, path integral method has been applied to the research of interest rate derivative pricing  [8]}, [9]}.
